The multiplicative domain in quantum error correction

Abstract

We show that the multiplicative domain of a completely positive map yields a new class of quantum error correcting codes. In the case of a unital quantum channel, these are precisely the codes that do not require a measurement as part of the recovery process, the so-called unitarily correctable codes. Whereas in the arbitrary, not necessarily unital case they form a proper subset of unitarily correctable codes that can be computed from properties of the channel. As part of the analysis we derive a representation theoretic characterization of subsystem codes. We also present a number of illustrative examples.

17 pages, preprint version

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• Spectral Properties of Tensor Products of Channels
• Open-System Quantum Error Correction
• Quantum Complementarity and Operator Structures
• Nullspaces of Entanglement Breaking Channels and Applications
• Quantum information theory and Fourier multipliers on quantum groups
• Zero-error communication under discrete-time Markovian dynamics
• A Multiplicative Ergodic Theorem for Bistochastic Ergodic Quantum Processes with Applications to Entanglement